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The repeating sequence of digits is called "repetend" which has a certain length greater than 0, also called "period". [4] In base 10, a fraction has a repeating decimal if and only if in lowest terms, its denominator has any prime factors besides 2 or 5, or in other words, cannot be expressed as 2 m 5 n, where m and n are non-negative integers.
Vinculum (symbol) repeated 0.1428571428571428571... A vinculum (from Latin vinculum 'fetter, chain, tie') is a horizontal line used in mathematical notation for various purposes. It may be placed as an overline or underline above or below a mathematical expression to group the expression's elements. Historically, vincula were extensively used ...
The duodecimal system, also known as base twelve or dozenal, is a positional numeral system using twelve as its base. In duodecimal, the number twelve is denoted "10", meaning 1 twelve and 0 units; in the decimal system, this number is instead written as "12" meaning 1 ten and 2 units, and the string "10" means ten.
1 ns: The time light takes to travel 30 cm (11.811 in) 10 −6: microsecond: μs One millionth of one second 1 μs: The time needed to execute one machine cycle by an Intel 80186 microprocessor 2.2 μs: The lifetime of a muon 4–16 μs: The time needed to execute one machine cycle by a 1960s minicomputer: 10 −3: millisecond: ms One ...
The reciprocals of prime numbers have been of interest to mathematicians for various reasons. They do not have a finite sum, as Leonhard Euler proved in 1737. Like rational numbers, the reciprocals of primes have repeating decimal representations. In his later years, George Salmon (1819–1904) concerned himself with the repeating periods of ...
This is also a repeating binary fraction 0.0 0011... . It may come as a surprise that terminating decimal fractions can have repeating expansions in binary. It is for this reason that many are surprised to discover that 1/10 + ... + 1/10 (addition of 10 numbers) differs from 1 in binary floating point arithmetic. In fact, the only binary ...
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/ x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a / b is b / a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one ...
The time of day is sometimes represented as a decimal fraction of a day in science and computers. Standard 24-hour time is converted into a fractional day by dividing the number of hours elapsed since midnight by 24 to make a decimal fraction. Thus, midnight is 0.0 day, noon is 0.5 d, etc., which can be added to any type of date, including (all ...
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